Since soil water depletion and salinity are major constraints for crop production, rice straw mulch could be beneficial for increasing yield and water productivity due to its role in conserving soil water and decreasing soil salinity. Two field experiments were conducted on a saline, silty clay soil to determine the effects of mulch and irrigation on the dynamics of soil water content and soil salinity, and on the growth and yield of sunflower sown by strip planting. In 2017, the mulching treatments were: no mulch (NM), rice straw mulch (RS) and retaining 15–20% of the crop residue of the previous rice crop (RR). In 2018 three irrigation treatments: one (I1), two (I2) and three irrigation events (I3), and two mulching treatments (NM and RS) were tested. In both years, the average gravimetric soil water content (SWC) was higher and topsoil salinity (EC1:5) was lower under RS treatment at 0−7 and 7−15 cm depth than with the NM treatment. The substantially higher solute potential of the soil solution in the surface soil with the RS treatment at 0−7 and 7−15 cm (−644 and −588 kPa in 2017, and -649 and −558 kPa in 2018) than with NM treatment (−925 and −728 kPa in 2017, and -801 and −641 kPa in 2018) was associated with increased grain yield (2.7 and 2.5 t ha−1 in 2017 and 2018, respectively). In the second year, the increasing number of irrigation events also increased yield, but the effects were additive to those of mulch. We conclude that the application of a rice straw mulch to the surface of saline-clay soils under strip planting can increase the solute potential of the soil solution thereby improving the growth and yield of sunflower.